XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,996,263

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2019, 5:07:05 AM Β· Difficulty 11.2615 Β· 3,835,633 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
52152a6c4aa1777a13024f6163196fa20fcd45ac0ba25c134a9a2227a05da0dd
View on Chainz β†—

Height

#2,996,263

Difficulty

11.261465

Transactions

1

Size

201 B

Version

2

Bits

0b42ef60

Nonce

455,961,098

Timestamp

1/5/2019, 5:07:05 AM

Confirmations

3,835,633

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

307729e014be07b9849002460f272c78bf0935fb9a50e1828286565200a631ac
Transactions (1)
Coinbase307729e014be07…86565200a631ac
1 in β†’ 1 out7.8700 XPM109 B
AUhjokok…k5m93PZR
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519039
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.474 Γ— 10⁹⁹(100-digit number)
24749839967434467891…53676584467522519041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.949 Γ— 10⁹⁹(100-digit number)
49499679934868935782…07353168935045038079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.949 Γ— 10⁹⁹(100-digit number)
49499679934868935782…07353168935045038081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
9.899 Γ— 10⁹⁹(100-digit number)
98999359869737871565…14706337870090076159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.899 Γ— 10⁹⁹(100-digit number)
98999359869737871565…14706337870090076161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.979 Γ— 10¹⁰⁰(101-digit number)
19799871973947574313…29412675740180152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.979 Γ— 10¹⁰⁰(101-digit number)
19799871973947574313…29412675740180152321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.959 Γ— 10¹⁰⁰(101-digit number)
39599743947895148626…58825351480360304639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.959 Γ— 10¹⁰⁰(101-digit number)
39599743947895148626…58825351480360304641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.919 Γ— 10¹⁰⁰(101-digit number)
79199487895790297252…17650702960720609279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,899,290 XPMΒ·at block #6,831,895 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy